Let's break down and solve the problem in the image step by step.

Problem Description:

1. Illumination sensors are used in applications such as outdoor lighting, which turns on automatically when it detects a certain light level.
2. The typical thresholds for turning on the lights are 10–20 lux, 20–30 lux, and 30–50 lux, with the most common illumination level used being 20–30 lux.

You are asked to calculate the current $I$ generated by the sensor when the incident illuminance is $E = 25 \, \text{lux}$ and the sensor sensitivity $\eta = 0.45 \, \frac{\text{mA}}{\text{lux}}$.

Formula:

The sensor produces a current proportional to the illuminance, given by the formula:

$I = \eta \cdot E$

Where:

• $I$ = current generated by the sensor,
• $\eta = 0.45 \, \frac{\text{mA}}{\text{lux}}$ is the sensitivity of the sensor,
• $E = 25 \, \text{lux}$ is the illuminance incident on the sensor.

Solution:

Substitute the values into the formula:

$I = 0.45 \, \frac{\text{mA}}{\text{lux}} \times 25 \, \text{lux}$

$I = 11.25 \, \text{mA}$

Thus, the current produced by the sensor is 11.25 mA.

Additional Question:

You're also asked to select the illumination range in which the sensor operates. Given that $E = 25 \, \text{lux}$, it falls within the range 20–30 lux, which is mentioned as one of the most commonly used illumination levels.

Would you like more details about the solution or any clarifications?

Here are 5 questions to further your understanding:

1. How is the sensitivity of an illumination sensor typically measured?
2. What real-world applications might require different lux thresholds for activation?
3. Why is the range of 20–30 lux commonly used in outdoor lighting?
4. How could sensor sensitivity change over time or with temperature?
5. What might happen if a sensor with a different sensitivity is used in this scenario?

Tip:

Make sure to check the unit consistency when using physical formulas, as mismatched units can lead to incorrect results.